Price of Fairness in Short-Term and Long-Term Algorithmic Selections

TL;DR

This paper analyzes the trade-offs between fairness and utility in sequential decision-making, revealing that short-term fairness constraints can cause long-term disparities, but simple policies can mitigate this.

Contribution

It introduces a theoretical framework for understanding the Price of Fairness in sequential settings and demonstrates how simple policies can reduce long-term disparities.

Findings

Short-term fairness constraints may increase long-term disparities.

Long-term disparities can be eliminated with simple investment policies.

Empirical validation confirms theoretical insights on synthetic and real data.

Abstract

Algorithmic decision-making in high-stakes settings can have profound impacts on individuals and populations. While much prior work studies fairness in static settings, recent results show that enforcing static fairness constraints may exacerbate long-run disparities. Motivated by this tension, we study a stylized sequential selection problem in which a decision-maker repeatedly selects individuals, affecting both immediate utility and the population distribution over time. We introduce notions of group fairness for both the short and long term and theoretically analyze the trade-off between fairness and utility via the Price of Fairness (PoF). We characterize optimal and fair policies in the short term and show that the PoF can be large even when group distributions are nearly identical. In contrast, we show that long-term disparities can vanish under simple investment policies that achieve a low PoF. We also empirically validate these theoretical observations using both synthetic and real datasets.